Abstract
The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.
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References
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Ahmad, A. Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions. Celestial Mech Dyn Astr 61, 181–196 (1995). https://doi.org/10.1007/BF00048514
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DOI: https://doi.org/10.1007/BF00048514